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First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method

  • In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of presolving as part of a parallel interior-point method to solve linear programs with block-diagonal structure, including both linking variables and linking constraints. While presolving reductions are often mathematically simple, their implementation in a high-performance computing environment is a complex endeavor. We report results on impact, performance, and scalability of the resulting presolving routines on real-world energy system models with up to 700 million nonzero entries in the constraint matrix.

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Author:Ambros GleixnerORCiD, Nils-Christian KempkeORCiD, Thorsten KochORCiD, Daniel RehfeldtORCiD, Svenja Uslu
Document Type:In Proceedings
Parent Title (English):Operations Research Proceedings 2019
First Page:105
Last Page:111
Publisher:Springer International Publishing
Tag:block structure; energy system models; high performance computing; interior-point method; linear programming; parallelization; preprocessing; presolving
MSC-Classification:90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C05 Linear programming
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C06 Large-scale problems
Year of first publication:2020
Page Number:XV, 819
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